Rewrite the equation by completing the square. $4 x^{2} +20 x +25 = 0$ $(x + $
Solution: $\begin{aligned} 4 x^2 +20 x +25&=0 \\\\ 4 x^2 +20 x &=-25 \\\\ x^2 +5 x&=-\dfrac{25}{4} \end{aligned}$ Now we want to complete $x^2 +5 x$ into a perfect square. To do that, we should add $\left(\dfrac{{5}}{2}\right)^2={\dfrac{25}{4}}$ to it: $x^2{+5}x + {\dfrac{25}{4}}=\left(x +\dfrac{5}{2} \right)^2$ $\begin{aligned} x^2 +5 x&=-\dfrac{25}{4} \\\\ x^2 +5 x + {\dfrac{25}{4}}&=-\dfrac{25}{4} + {\dfrac{25}{4}} \\\\ \left(x +\dfrac{5}{2} \right)^2&=0 \end{aligned}$ In conclusion, the equation after completing the square is written as: $\left(x +\dfrac{5}{2} \right)^2=0$